Time
Unless you are very sure that your still is completely safe and self sufficient, it is a very good idea to stay near by while distillation is in progress. Distillation can be very slow (read days), depending on many factors. More details below.

Method

Intro
There are two main types of hard liquor that you can make. The easiest to make of the two is a brandy-like liquor. This keeps much of the flavor of the original home brew. The second is to make a vodka-like drink that is basically just alcohol and water. You can add various essences (available at many brewing shops) or other flavoring substances to the vodka-like drink to make it taste more interesting. If you know how to do this well, you can make really great liqueurs such as contreau.

Important Warning
Don't drink anything till you've finished the whole process and mixed your liquor. Imagine this situation: You watch the first glass of liquor come out of your still and decide to drink it down. Bad move! You then are quite likely to fall very sick, end up in hospital or die. The reason is that you get the most potent and alcohol rich liquid over first. The first glass out of a 5L batch contains most of the bad stuff like wood alcohol and other low atomic weightcarbon compounds, not to mention an extremely high ethanol content.

For Brandy-like liquor
Distill very slowly. To distill 5 liters, it should take you at least half a day. Keep the first 5% or so of the stuff that comes over separate. It's a bad idea to drink this. See above warning. It is very potent stuff. It won't freeze in the freezer and if you light it, it should burn with a almost totally blue or colorless flame. Keep distilling till the distillate that comes over starts to looks a bit oily. You've now distilled just about all of the good stuff from your home brew. Throw away the low alcohol yuck that remains in the bottom of the still. Now, distill the distillate. Keep all of the second round distillate - don't ditch the first 5% or anything like that. Keep distilling till about 3/4 of the first round distillate has come across. Throw away the remains of the first round distillate. You should have about 1L of colorless second round distillate. It'll be somewhere around 40% alcohol (80% proof), assuming you started with home brew with around 12% alcohol. Sample your brandy-like liquor. If it still tastes harsh, you might want to add some water or distill it another time. And there you go! Don't drink it all on the same day :) (The cautious may want to drink a little one day and see if they feel sick before committing more fully!). Now, try to think of a cool name for your new liquor!

For Vodka-like liquor
Start with brandy-like liquor. Keep distilling over and over until the distillate has very little flavor. If you don't want to drink it like that, you can turn it into a liqueur. I once made a lemon liqueur which was quite nice. Mainly liquor, lemon juice, lemon rind and sugar mixed together and left alone for about a month.

Closing notes
Distillation is illegal in lots of countries. See legality of distilling at home. Also, you can burn yourself if you have a bad still or do something silly like waving flames near the still. It's also possible to poison yourself by drinking too much of your own liquor. If you have made 1/5 as much hard liquor as the amount of home brew you started with, only drink 1/5 as much, if that!
Warnings aside, distilling is great fun and very rewarding. Cheers!